Abstract

In insulating materials with ordered magnetic spiral phases, ferroelectricity can emerge owing to the breaking of inversion symmetry. This property is of both fundamental and practical interest, particularly with a view to exploiting it in low-power electronic devices. Advances toward technological applications have been hindered, however, by the relatively low ordering temperatures Tspiral of most magnetic spiral phases, which rarely exceed 100 K. We have recently established that the ordering temperature of a magnetic spiral can be increased up to 310 K by the introduction of chemical disorder. Here, we explore the design space opened up by this novel mechanism by combining it with a targeted lattice control of some magnetic interactions. In Cu-Fe layered perovskites, we obtain Tspiral values close to 400 K, comfortably far from room temperature and almost 100 K higher than using chemical disorder alone. Moreover, we reveal a linear relationship between the spiral’s wave vector and the onset temperature of the spiral phase. This linear law ends at a paramagnetic-collinear-spiral triple point, which defines the highest spiral ordering temperature that can be achieved in this class of materials. On the basis of these findings, we propose a general set of rules for designing magnetic spirals in layered perovskites using external pressure, chemical substitutions, and/or epitaxial strain, which should guide future efforts to engineer magnetic spiral phases with ordering temperatures suitable for technological applications.

INTRODUCTION

Magnetic frustration is characterized by the magnetic interactions that cannot be simultaneously satisfied (1–6) and may lead to nontrivial magnetic orders (7–11). An example of these exotic magnetically ordered phases is the spin spiral, which has received a lot of attention during the last decade because of its potential for inducing ferroelectricity in insulating materials (12–16). Stabilization of the spiral state close to room temperature (RT) is a necessary condition to use this property for magnetoelectric applications. Unfortunately, very few insulators display spiral phases above 100 K.

Besides cupric oxide (CuO) and some hexaferrites (17–20), the layered perovskite YBaCuFeO5 is one of the few exceptions to this rule. However, what makes this last material truly remarkable is the extraordinary tunability of its spiral ordering temperature (Tspiral), which can be increased by more than 150 K by manipulating the Cu/Fe chemical disorder in the structure. We showed recently that Tspiral can be shifted from 154 to 310 K by adjusting the average Cu/Fe occupations nCu and nFe of the square-pyramidal sites in the crystal unit cell (Fig. 1A) (21). We also established the existence of a positive correlation between the spiral ordering temperature and the degree of Cu/Fe intermixing (maximal for nCu = nFe = 50%). However, the most surprising observation is that tiny differences in the Cu/Fe occupations (|nCu − nFe| ≤ 6%) can shift Tspiral by more than 150 K. Such a huge positive impact of the Cu/Fe disorder in the spiral stability is remarkable and calls for further investigations aimed at both understanding and exploiting this unusual trend.

Fig. 1Link between Cu/Fe chemical disorder and magnetic order in YBaCuFeO5.

(A) Crystal structure of YBaCuFeO5 with Cu/Fe disorder in the bipyramidal sites. Jc1 and Jc2 denote the nearest-neighbor (NN) antiferromagnetic (AFM) and ferromagnetic (FM) couplings, respectively, along the c axis, and Jab denotes the average NN AFM coupling in the ab plane. (B) Schematic representation of the correlated Cu-Fe chemical disorder in YBaCuFeO5, characterized by the presence of randomly disordered Cu-Fe FM “dimers.” (C) Magnetic structure of the commensurate collinear phase. (D) Magnetic structure of the incommensurate spiral phase. (E) The representation of (B) in terms of magnetic bonds. The impact of a few strong, randomly distributed AFM Fe-Fe “defects” is illustrated by the gray ellipses, which delimit the regions where the Cu-Fe spins lose their collinearity. Thinner bonds represent weak AFM or FM couplings, while thicker bonds indicate strong AFM couplings. The cross-talking of these regions eventually gives rise to a spiral if the in-plane separation of the Fe-Fe impurities is smaller than ξmin. Note that the same number of weakly interacting Cu-Cu “defects” is necessary to preserve the material’s stoichiometry. The J values are those of Scaramucci et al. (32).

The aim of the present study is to explore the design space opened by this novel, disorder-based spiral control mechanism. After having shown its potential and limitations for the particular case of YBaCuFeO5 (21), we combine it here with a targeted lattice tuning of some magnetic exchanges. The idea behind this is to add up the effect of both mechanisms to stabilize spin spirals at temperatures higher than those obtained using these two strategies separately. In the following, we show that, for Cu-Fe–based layered perovskites, Tspiral values close to 400 K can be obtained using this approach. These values are ~100 K higher than using chemical disorder alone (21) and expand the stability range of the spiral to a comfortable temperature region that extends well beyond RT. We also uncover the existence of an intriguing paramagnetic-collinear-spiral triple point, which defines the highest Tspiral value that can be achieved in this class of materials. Moreover, we find several correlations between the spiral properties and some structural parameters that can be summarized in the form of a simple set of rules for magnetic spiral design in layered perovskites. Besides overcoming limiting factors in terms of operating temperatures, these results could contribute to increase the number of materials featuring spiral phases that are stable well beyond RT and be an important step toward the technological application of magnetic spirals in spintronic devices.

The strategy followed to attain our goal is based on the particularities of the YBaCuFeO5 crystal structure and the associated NN exchange couplings. A schematic representation of the layered perovskite unit cell of this material (space group P4mm) is shown in Fig. 1A (22–24). The A sites are occupied by equal amounts of Y3+ and Ba2+ that order in planes perpendicular to the c axis owing to their very different ionic radii (25). The B sites host Fe3+ and Cu2+ in a square-pyramidal coordination that forms slabs of “bowties” separated by Y3+ layers. In contrast to Y and Ba, Cu and Fe display a very particular kind of correlated disorder, which is characterized by the preferential occupation of the bowties by Cu-Fe pairs (24). These Cu-Fe dimers are disordered in the structure (see Fig. 1B), leading to variable, preparation-dependent averaged Cu/Fe occupations of the atomic positions inside the pyramids.

The Cu-Fe dimers have very important consequences for the magnetism of YBaCuFeO5. As demonstrated in (24, 26), all possible in-plane NN interactions Jab (Fe-Fe, Cu-Cu, and Cu-Fe) are strong and AFM (see Fig. 1, A and B). Jc1, one of the two NN couplings along the c axis (Fig. 1, A and C), is also AFM and disorder independent, but its value is about one order of magnitude smaller. The intra-bowtie coupling Jc2, comparable to Jc1 in absolute value, is the only FM NN exchange interaction, and it is worth noting that this is only possible if the bowties are preferentially occupied by Cu-Fe pairs (i.e., if Jc2 = JCu-Fe) (24). This set of magnetic interactions is at the origin of the collinear magnetic phase observed at high temperatures (T < Tcollinear) with kc = (1/2, 1/2, 1/2) (see Fig. 1C) (21, 24, 27–30). Note that despite the underlying chemical disorder, the preferential occupation of the bowties by FM Cu-Fe dimers and the nondependence of the sign of Jab and Jc1 with the Cu/Fe disorder imply that the magnetic structure can be seen as a set of ordered layers with strong in-plane AFM bonds coupled through weak, alternating FM and AFM bonds along the c axis (Fig. 1E).

At low temperatures, the kz component of the propagation vector becomes incommensurate and the collinear magnetic order transforms into an inclined circular spiral with ki = (1/2, 1/2, 1/2 ± q) (Fig. 1D) (21, 24, 28, 29, 31). Although the c axis seems naturally more prone to a magnetic instability owing to the weakness of Jc1 and Jc2, the appearance of the spiral state is surprising because these two couplings are not frustrated, and the next-NN interactions, estimated from density functional theory (DFT) calculations, either are too small or have the wrong sign to produce frustration along this direction (24, 26, 32, 33).

RESULTS

Tuning Tspiral with chemical disorder

Very recently, an alternative, disorder-based mechanism has been proposed by Scaramucci and co-workers (32). These authors demonstrated that a magnetic spiral can be stabilized through the introduction of a few strong, randomly distributed frustrating bonds in systems featuring a single crystallographic direction with weak NN magnetic couplings. YBaCuFeO5, with strong in-plane couplings and weak, alternating AFM/FM exchanges along the c axis (Fig. 1B), fulfills these premises (24, 26). The required frustrating bonds are provided by small, preparation-dependent amounts of bowties occupied by Fe-Fe pairs (accompanied by the same amounts of Cu-Cu pairs if we assume a constant Cu/Fe ratio). Although both are energetically unfavorable (24), their presence at very low concentrations cannot be disregarded in real materials. Rather, the monotonic changes in the size of the bowties with increasing cooling rates suggest that their concentration could be directly linked to the degree of Cu/Fe disorder. Because of the small Cu2+ moment (S = 1/2) and the extremely weak Cu-Cu coupling (JCu-Cu ~ 0) (dashed bonds in Fig. 1E), a Cu-Cu defect is expected to have only a minor impact in the alignment of the neighboring spins. However, an AFM Fe-Fe pair (S = 5/2, JFe-Fe ~ −100 meV) (solid green bonds in Fig. 1E) constitutes an extremely strong local perturbation of the underlying collinear spin order, particularly along the c axis where the couplings are weak. This perturbation can extend to several unit cells (Fig. 1, B and E), become collective, and give rise to a spiral if (i) the Fe-Fe defects do not cluster within the ab plane, i.e., if they are separated by a minimal average distance ξmin; (ii) the JCu-Fe/JFe-Fe ratio is small enough and negative to guarantee strong local frustration; and (iii) the concentration of Fe-Fe defects n is low enough so as to avoid impurity bonds dominating the order between successive planes (n < JCu-Fe/JFe-Fe) (32, 33).

The main prediction of this model is that both the spiral ordering temperature Tspiral and the magnetic modulation vector q should increase linearly with n, as long as it remains at these low levels (32). This is qualitatively verified in YBaCuFeO5 samples prepared with different cooling rates, where the highest q and Tspiral values are observed for the samples quenched in liquid nitrogen (i.e., those with the largest Cu/Fe disorder and where n is expected to be the highest; see Fig. 2A) (21). It also suggests that the spiral ordering temperature could be further increased if a slightly larger value of n could be achieved. Since faster cooling rates are not easily achieved experimentally, we explore here an alternative strategy based on the combination of the highest possible Cu/Fe chemical disorder with a targeted lattice tuning of some magnetic exchanges.

Fig. 2Stability of the collinear and spiral phases with different tuning parameters.

(A to C) Evolution of Tcollinear and Tspiral using different tuning parameters: (A) YBaCuFeO5 prepared with different cooling rates [adapted from (21)]. (B) Replacement of Y3+ by a rare-earth cation (RE3+). (C) Replacement of Ba2+ by Sr2+. The Tcollinear and Tspiral values are those determined from PND. The background color represents the z component of the magnetic propagation vector (kz), which changes from 1/2 in the collinear phase to 1/2 ± q in the spiral phase (only the 1/2 − q incommensurate satellite is used in the figures). (D to G) Signatures of the collinear and spiral phases in the PND patterns. The contour maps show the temperature dependence of the positions and the intensities of the commensurate (1/2, 1/2, 1/2) magnetic Bragg reflection and the incommensurate (1/2, 1/2, 1/2 ± q) satellites for the REBaCuFeO5 (D) and YBa1−xSrxCuFeO5 (F) series. The blue and red arrows indicate the ordering temperatures Tcollinear and Tspiral, respectively. The integrated intensities are shown in (E) for REBaCuFeO5 and in (G) for YBa1−xSrxCuFeO5. For the Sr-doped sample with x = 0.5, the “minus” incommensurate satellite (1/2, 1/2, 1/2 − q) was extremely weak (see also fig. S3). Hence, only the integrated intensity of the “plus” satellite (1/2, 1/2, 1/2 + q) is shown. The error bars of the integrated intensities are the SDs obtained from three Gaussian least-squares fits of the (1/2, 1/2, 1/2) Bragg reflection and its incommensurate satellites carried out using the Igor software. a.u., arbitrary units.

Adding the effect of the lattice

On the basis of the previous discussion, the main candidates that influence the degree of magnetic frustration at constant Cu/Fe disorder are the NN couplings Jc1 and Jc2 along the c axis, which we expect to display a negative correlation with the variation of the inter-bowtie separation (d1) and the bowtie size (d2), respectively (Fig. 1C) (21). Since large changes in these two interatomic distances can be achieved through isovalent A-cation substitutions, we prepared two series of layered perovskites aimed to tune them separately. In the first one, Y3+ was replaced by trivalent 4f cations RE3+ with growing ionic radius (REionic) with the purpose of acting on d1 (RE = Lu to Dy); in the second, Ba2+ was partially substituted by different amounts of smaller Sr2+ (0 ≤ x ≤ 0.5) with the aim of tuning d2. To add up the impact of both the lattice and the Cu/Fe disorder, we maximized this last parameter in all the samples, which were quenched in liquid nitrogen after the last annealing (see Materials and Methods).

The impact of this d1 tuning on Tspiral is illustrated in Fig. 2B, which also shows the evolution of Tcollinear with the rare-earth ionic radius in the REBaCuFeO5 series as determined from powder neutron diffraction (PND). The presence of the collinear and spiral phases in all samples was confirmed by the observation of magnetic Bragg reflections corresponding to kc = (1/2, 1/2, 1/2) and ki = (1/2, 1/2, 1/2 ± q) (Fig. 2, D and E, and figs. S1 and S2). The two transition temperatures change monotonically with REionic and display completely opposite behaviors, with Tcollinear decreasing and Tspiral increasing for larger ionic radii. The lowest spiral ordering temperature corresponds to LuBaCuFeO5 (213 K), and the highest corresponds to DyBaCuFeO5 (312 K). This last value, the only one above RT (39°C), is 2°C higher than the Tspiral reported in (21) for quenched YBaCuFeO5 (Fig. 2A).

The manipulation of d2 also has a strong impact on both transition temperatures. This is illustrated in Fig. 2C, where the evolution of Tcollinear and Tspiral in the YBa1−xSrxCuFeO5 family as a function of the Sr content x is shown. PND measurements again confirmed the existence of collinear and spiral phases with propagation vectors kc = (1/2, 1/2, 1/2) and ki = (1/2, 1/2, 1/2 ± q) in all the materials investigated (Fig. 2, F and G, and figs. S1 and S2). We note that, contrary to the predictions of Dey et al. (26), Tcollinear decreases with x. Tspiral displays the opposite behavior, reaching 375 K (102°C) for x = 0.4. Linear extrapolation indicates that both temperatures should merge at ~395 K for x ~ 0.49, giving rise to a paramagnetic-collinear-spiral triple point. For x = 0.5, i.e., just after this point, the sample enters into a different regime characterized by an abrupt change in the stability of the spiral state. As shown in Fig. 2F and fig. S3, the magnetic reflections associated to the propagation vector ki = (1/2, 1/2, 1/2 ± q) are still present, but they are extremely weak. Moreover, they coexist with a new, very strong reflection corresponding to the propagation vector kc′ = (1/2, 1/2, 0) and those of the kc = (1/2, 1/2, 1/2) collinear phase. These observations suggest that the spiral state is abruptly suppressed and replaced by a new AFM phase beyond the crossing of the Tcollinear and Tspiral lines.

The temperature dependence of q for the REBaCuFeO5 and YBa1−xSrxCuFeO5 series and that of YBaCuFeO5 prepared using different cooling rates (21) are shown in Fig. 3 (A to C). For the samples with the lowest Tspiral, we observe a smooth, continuous decrease of q characteristic of second-order phase transitions. This behavior is progressively replaced by an abrupt collapse of q in the samples with higher Tspiral, suggesting that the collinear-to-spiral transition changes from second to first order by approaching the Tspiral = Tcollinear point (fig. S3). The evolution of the spiral plane inclination (φG) and the q value (qG) at 10 K is shown in Fig. 3 (D to F). For the three series of samples, we observe a clear, positive correlation among Tspiral, φG, and qG. In each family, the highest Tspiral is observed for the sample with the largest φG, which reaches values close to 90° for RE = Dy. This corresponds to a perfect cycloid, indicating that the samples with the highest spiral ordering temperature have the potential of displaying the largest saturation polarization (15, 16). Establishing whether this is the case is beyond the scope of this study and will require further experimental and theoretical work.

Fig. 3Evolution of magnetic spiral properties with different tuning parameters.

(A to C) Temperature dependence of the magnetic modulation vector q in YBaCuFeO5 using different tuning parameters: (A) Cooling rate [adapted from (21)]. (B) Replacement of Y3+ by a rare-earth cation (RE3+). (C) Replacement of Ba2+ by Sr2+. (D to F) Evolution of Tspiral, the ground-state values (10 K) of the magnetic modulation vector (qG), and the inclination of the spiral rotation plane (φG) using different tuning parameters: (D) Cooling rate [adapted from (21)]. (E) Replacement of Y3+ by a rare-earth cation (RE3+). (F) Replacement of Ba2+ by Sr2+. The inset in (D) shows the definition of the inclination angle φG. The dashed lines are guides to the eye and indicate the positive correlation among Tspiral, qG, and φG. The values for REBaCuFeO5 and YBa1−xSrxCuFeO5 families were extracted from Rietveld fits of the DMC data recorded at 10 K (fig. S5). The error bars of qG and φG, listed in tables S2 and S3, are the SDs obtained from the fits of the magnetic structure using the FullProf Suite Rietveld package (50).

An interesting observation, common to all the samples investigated in this study, is the existence of a linear relationship between the ordering temperature and the ground-state periodicity of the spiral. This can be better appreciated in Fig. 4, where the evolution of Tspiral with qG for the three series of samples is shown. We note that the extrapolation of the linear law toward low Tspiral values crosses the origin (i.e., Tcollinear = 0 for qG = 0), whereas in the high qG side, Tcollinear and Tspiral converge to a common value of ~395 K for qG ~ 0.18. The sudden disappearance of the spiral and the observation of a new magnetic phase close to this point suggest the existence of a limiting value for both the spiral’s periodicity and ordering temperature. In other words, 395 K is most probably the highest Tspiral value that can be reached in Cu-Fe–based layered perovskites. To the best of our knowledge, it is the highest spiral ordering temperature reported for a transition metal oxide, the only comparable example being the Néel temperature of the transverse conical spiral phase in the hexaferrite Sr3Co2Fe24O41 [~400 K; see (19)]. Moreover, it is comfortably far from RT, an important point regarding applications, and almost 100 K higher than the highest Tspiral value previously reported for YBaCuFeO5 using chemical disorder alone (310 K).

Correlation between Tspiral and the ground-state magnetic modulation vector qG in three families of AA′CuFeO5 layered perovskites: YBaCuFeO5 prepared with different cooling rates [full blue symbols; data from (21)], REBaCuFeO5 with RE = Lu to Dy (full red symbols), and YBa1−xSrxCuFeO5 with 0 ≤ x ≤ 0.4 (full green symbols). The full black star corresponds to the (qG, Tspiral) point reported for a YBaCuFeO5 single crystal in (29). The Tcollinear values of all samples (open symbols) are also shown to illustrate its convergence with Tspiral at qG ~ 0.18. The Tspiral and Tcollinear values are those determined from PND (tables S1). The error bars of qG, listed in tables S2 and S3, are the SDs obtained from the fits of the magnetic structure using the FullProf Suite Rietveld package (50), and they are smaller than the marker’s size.

Chemical disorder versus lattice tuning

After demonstrating the success of our combined approach, we investigate in detail the associated changes in the crystal structure with the aim of obtaining additional insight into their link with the degree of magnetic frustration. We use high-resolution PND (fig. S6) to obtain precise values of the different structural parameters for the REBaCuFeO5 and YBa1−xSrxCuFeO5 series, which we compare with those obtained for YBaCuFeO5 prepared using different cooling rates (21). We first check the average Cu/Fe occupancies nCu and nFe of the bipyramidal sites, which we expected to be very similar owing to the quenching procedure used during the synthesis. The obtained values, shown in Fig. 5 (A to C) and tables S2 and S3, confirm a high degree of disorder in all the samples, which display average Cu/Fe occupancies very close to 50%.

(A to U) Evolution of selected structural parameters as a function of the cooling rate [YBaCuFeO5; data from (21)], the rare-earth ionic radius (REBaCuFeO5), and the Sr content x (YBa1−xSrxCuFeO5). (A to C) Average Cu/Fe occupation in the pyramids. (D to I) Lattice parameters a and c. (J to L) Tetragonal distortion c/2a. (M to O) Distance d1 between the bipyramidal layers along the c axis. (P to R) Thickness d2 of the bipyramidal layers. (S to U) d1/d2 ratio. (V) Evolution of Tspiral with d1/d2 ratio. The yellow, red, and green colors correspond to YBaCuFeO5 prepared with different cooling rates, REBaCuFeO5 (RE = Lu to Dy), and YBa1−xSrxCuFeO5 (x = 0 to 0.4), respectively. The Tspiral and Tcollinear values are those determined from PND (tables S1). The dashed lines are guides to the eye. All structural parameters were extracted from the Rietveld fits of the high-resolution PND data at RT (tables S2 and S3). The error bars are the SDs provided by the FullProf Suite Rietveld package (50).

The evolution of the lattice parameters and the tetragonal distortion c/2a for the three series are summarized in Fig. 5 (D to L). On the basis of the results obtained for YBaCuFeO5 with different degrees of Cu/Fe disorder, we established in (21) an empirical, positive correlation between c/2a and Tspiral and suggested the use of this parameter for Tspiral control purposes. Although a similar correlation was observed for the REBaCuFeO5 series (Fig. 5K), Fig. 5L reveals the opposite behavior in the Sr-substituted family. This suggests that the use of c/2a for the control of magnetic frustration, of potential interest in thin film growth, cannot be generalized to all Cu/Fe layered perovskites.

We investigate now the presence of correlations between Tspiral and the different NN interatomic distances and angles. In fig. S4, we have represented the evolution of the average in-plane Cu/Fe-O distance and the average superexchange angle for the three families. As for the lattice parameters, Tspiral does not display a monotonic behavior with any of those parameters. We thus conclude that the in-plane distances and angles are not suitable parameters for controlling the spiral ordering temperature. The modification of the inter- and intra-bowtie distances d1 and d2 along the c axis and their ratio d1/d2 for the three series are summarized in Fig. 5 (M to U). The longest d1 and shortest d2 values are systematically observed in the three families for the samples with the highest Tspiral and lowest Tcollinear values. Moreover, the d1/d2 ratio displays a positive correlation with the spiral ordering temperature in the three series. This common behavior indicates that, contrary to c/2a, the d1/d2 ratio is a good parameter for the control of magnetic frustration in Cu/Fe-based layered perovskites.

Despite a common positive correlation between Tspiral and d1/d2 ratio, Fig. 5 unravels the existence of large differences among the structural modifications in the three series. The smallest changes in the lattice parameters and the interatomic distances correspond to the YBaCuFeO5 samples with different degrees of Cu/Fe disorder. These tiny variations give rise to changes in Tspiral of more than 150 K, much larger than those in the REBaCuFeO5 (~100 K) and YBa1−xSrxCuFeO5 (~90 K) series, where the variation of the lattice parameters and interatomic distances is much more pronounced. This is better appreciated in Fig. 5V, where the evolution of Tspiral with d1/d2 is displayed. This parameter, which reflects the relative strength Jc2/Jc1 of the couplings along the c axis, changes very little in the YBaCuFeO5 samples with different degrees of disorder (0.41%). However, it increases by more than 1.7% between the two extremes of the YBa1−xSrxCuFeO5 family and by 4.6% in the REBaCuFeO5 series. These results confirm the exceptional efficiency of chemical disorder alone for Tspiral tuning. On the other side, our data also show that a comparable efficiency in terms of Tspiral increase can be reached at a fixed degree of chemical disorder by acting exclusively on the lattice. A particularly interesting observation is that the impact of both mechanisms on the spiral ordering temperature is additive: Once the highest Tspiral value is reached by manipulating the Cu/Fe disorder, it can be further increased through the maximization of the d1/d2 ratio. This allows Tspiral tuning over unprecedentedly large temperature ranges, providing, at the same time, a versatile tool for stabilizing spin spirals at temperatures well beyond RT.

Experiment versus theory

Having presented the experimental facts, we now compare our observations with the predictions of the random frustrating bonds (RFB) model proposed by Scaramucci and co-workers (32, 33). The main prediction of this model is that both Tspiral and q should increase with the concentration of Fe-Fe frustrating bonds n. Since n is in turn correlated with the degree of average Cu/Fe disorder, this prediction explains well the behavior reported for the YBaCuFeO5 samples prepared with different cooling rates (21). However, it is difficult to conciliate the huge Tspiral changes observed in the YBa1−xSrxCuFeO5 and REBaCuFeO5 families, where the Cu/Fe disorder was kept approximately constant. A similar situation is observed with a second prediction, namely, the existence of a proportionality law between Tspiral and qG. This linear law should be verified by samples with different degrees of disorder, and this is indeed the case for the YBaCuFeO5 series prepared with different cooling rates (full blue circles in Fig. 4) (21). More intriguing is the fact that the very same law is also verified by the YBa1−xSrxCuFeO5 (full green pentagons) and REBaCuFeO5 families (full red diamonds) and even by the YBaCuFeO5 single crystal from (29) (black star) to a very good approximation. This unexpected observation cannot be explained within the framework of the RFB model and calls for the explicit consideration of lattice’s impact in the different magnetic exchanges.

A third point needing further theoretical work is the origin of the intersection of Tspiral and Tcollinear for qG ~ 0.18 and the sudden replacement of the spiral state by a second commensurate AFM phase beyond this point. Given that it coincides with the smallest d2 (i.e., largest Jc2) values of our study, the disappearance of the spiral could be tentatively ascribed to the point where the AFM couplings between Fe-Fe impurities become so large that the FM coupling of the bipyramids occupied by Cu-Fe pairs can no longer compete and the magnetic frustration is suppressed. The result would be a magnetic structure where all NN couplings are AFM, in agreement with the observation of the new magnetic propagation vector kc′ = (1/2, 1/2, 0). However, it is not clear why this point should coincide with the intersection of the Tcollinear and Tspiral lines. Another intriguing observation is the continuous evolution of the spiral-to-collinear phase transition from second to first ordering by approaching the paramagnetic-collinear-spiral triple point. Information about the behavior of the different magnetic phases beyond the crossing of the Tcollinear and Tspiral lines should help to understand its exact nature and, in particular, to clarify whether we could be in the presence of a Lifschitz point (34, 35). We also note that its increased entropy at the crossing makes this point potentially interesting for the search of exotic magnetic states in the presence of external perturbations such as magnetic fields or elevated pressures (34, 36, 37).

Toward spiral design in layered perovskites

An important outcome of the structural property correlations presented in previous sections is that they enable the proposal of a simple set of rules for the design of high-temperature magnetic spirals in other AA′BB′O5 layered perovskites with B-site disorder. Besides maintaining electric neutrality, the most critical point is to identify B/B′ cation pairs of comparable sizes and affinity for square-pyramidal coordination. They should be also capable of producing weak, alternating FM and AFM couplings along the c axis, and large in-plane exchange constants, with a very large value for one of the two JBB or JJBB′ couplings. The choice is mostly limited by the relatively small number of pairs resulting in FM coupling within the pyramids, but among 3d transition metals, Cu2+/Cu3+, Cu2+/Co3+(high spin), Cu2+/Mn3+, or Mn2+/Co3+(low spin) could be possible candidates if JBB and JB′B′ have the appropriate absolute values. Ab initio DFT estimations of the magnetic exchanges, particularly for 4d and 5d pairs, will be highly desirable and shall increase the number of potential candidates. The choice of the A/A′ cations requires ionic radii different enough to stabilize the layered perovskite structure. However, the highest Tspiral values can be achieved when the ionic radius of the A cation close to the apical oxygen is small and the rAionic – rA′ionic difference is as small as possible (Fig. 5). Concerning thin-film design, we saw that c/2a alone is not a good parameter for Tspiral control. Hence, high Tspiral values can be a priori stabilized under both tensile and compressive strain as long as the rules concerning the choice of the A and B cations are fulfilled.

We can also speculate on the expected behavior of Tspiral under external pressure. According to our findings, this will depend on the behavior of d1/d2, i.e., on the relative compressibility of these two distances. In general, bonds involving cations with high coordination or low valence expand or compress faster than those with cations in low coordination or with high valence (38, 39). d2, involving 12 (Ba2+–O2−) bonds, is thus expected to compress faster than d1, where only 8 (RE3+–O2−) bonds contribute. Since this will result in a smaller d1/d2 ratio, a decrease of Tspiral is thus predicted under the application of external pressure.

To summarize, we have experimentally validated an emerging route for stabilizing spin spirals up to temperatures far beyond RT. Our approach, based on the combination of chemical disorder with a targeted lattice tuning of some magnetic exchanges, takes full advantage of the additivity of these two mechanisms. As a result, the stability domain of the spiral magnetic order can be tuned over unprecedentedly large temperature ranges. In the particular case of Cu/Fe-based layered perovskites, we demonstrate that Tspiral values close to 400 K can be reached using this strategy. This value is ~100 K higher than using chemical disorder alone (21) and comfortably far beyond RT. We also reveal the existence of a linear relationship between the spiral’s ordering temperature and periodicity, a paramagnetic-collinear-spiral triple point, as well as several correlations between the spiral properties and some structural parameters. We discuss these results in light of a recently proposed RFB-based mechanism and propose a simple set of rules for the design of magnetic spirals in isostructural layered perovskites by using external pressure, chemical substitutions, or epitaxial strain. Besides overcoming one of the main hindrances for applications, these results could accelerate the discovery of other materials featuring spiral phases stable well beyond RT, paving the way toward the long-sought technological use of magnetic spirals in spintronic devices.

MATERIALS AND METHODS

Materials synthesis

The REBaCuFeO5 and YBa1−xSrxCuFeO5 polycrystalline samples were prepared using the solid-state reaction method. High-purity RE2O3 or Y2O3 (99.995 to 99.998%; Aldrich/Alfa Aesar), SrCO3 (99.995%; Aldrich), BaCO3 (99.997%; Alfa Aesar), CuO (99.995%; Alfa Aesar), and Fe2O3 (99.998%; Alfa Aesar) powders were used as starting materials. Dehydrated rare-earth oxide powders were obtained by heating them at 1223 K for 15 hours. The required stoichiometric amounts of RE2O3, SrCO3, BaCO3, CuO, and Fe2O3 were then weighted, thoroughly grounded, and heated at a rate of 300 K/h up to the synthesis temperature Ts (= 1323 to 1430 K), which was optimized for every sample using thermogravimetric analysis under He/O2 gas flow. The powders were then annealed for 50 hours at this temperature under oxygen gas flow. The obtained materials were cooled in the furnace down to RT, thoroughly grounded again, pressed into pellets, and sintered at Ts for another 50 hours. After this treatment, all samples were quenched into liquid nitrogen. Small pieces were kept solid for their use in magnetization measurements, and the rest were pulverized and subsequently used in PND experiments. The phase purity of all samples was checked using laboratory powder x-ray diffraction at RT using a Bruker D8 Advance diffractometer with Cu Kα radiation. All samples were very well crystallized and free of impurities within the limit of this technique (~1%).

Magnetic susceptibility

DC magnetization (M) measurements were performed in a superconducting quantum interference device magnetometer (MPMS-XL 7T, Quantum Design). Small pellets (diameter ~ 3 mm, height ~ 1 mm, mass ~ 15 to 25 mg) from the same batches as the samples used for the PND measurements were measured between 2 and 400 K by heating under a magnetic field of μ0H = 0.5 T after being cooled down to 2 K in zero field. The magnetization was further measured between 300 and 600 K using a high-temperature insert. The samples, mounted on transparent drinking straws for the measurements below 400 K, were dismounted and wrapped in aluminum foil as described in (40) for the measurements above this temperature. The signal from the aluminum foil, measured separately, was found to be temperature independent and negligible when compared with the sample’s magnetization. For the samples with magnetic RE3+ cations, the magnetic transitions from the Cu/Fe sublattice are difficult to observe in the magnetization data because of the large paramagnetic contribution of the RE3+ moments, and they have been missed in some previous studies (41). However, they can still be tracked in the first derivatives of the DC inverse susceptibility 1/χDC = H/M (fig. S1). The values of Tcollinear and Tspiral derived from this technique correspond to the midpoint of the step-like anomalies in the 1/χDC derivative, which coincides with the χDC maximum in the YBa1−xSrxCuFeO5 series.

Although the REBaCuFeO5 samples were also synthesized in the past (42, 43), the existence of magnetic transitions has only been reported for a few of them (41, 44–47), and there is no apparent systematics between the reported ordering temperatures and the RE ionic radii. A similar situation was observed in the YBa1−xSrxCuFeO5 series, where the presence of spiral phases was either disproven (48) or not demonstrated (49) in previous studies. As shown in Fig. 2C, this is not the case in this study, where the collinear and spiral phases are observed for all samples. Moreover, Tcollinear and Tspiral change in a monotonic way as a function of both the RE ionic radius and the Sr content x.

Differential scanning calorimetry

The paramagnetic-to-collinear phase transition at Tcollinear was also measured by differential scanning calorimetry (DSC) for REBaCuFeO5 and YBa1−xSrxCuFeO5 powder samples by using a NETZSCH DSC 204F1 device. Fine powders (mass, ~30 mg) were sealed into aluminum crucibles and heated up to 670 K with a rate of 15 K/min under Ar gas flow. The data were acquired during the heating process (see fig. S2).

Powder neutron diffraction

PND measurements were carried out at the Swiss Spallation Neutron Source (SINQ) of the Paul Scherrer Institute in Villigen, Switzerland, and the Institut Laue-Langevin (ILL) in Grenoble, France. The REBaCuFeO5 and YBa1−xSrxCuFeO5 powder samples were introduced in cylindrical vanadium cans (diameter = 6 mm, height = 5 cm) and mounted on the stick of a helium cryostat (2 to 300 K) and a cryofurnace (2 to 500 K). PND patterns were continuously recorded at the powder diffractometer DMC (cold neutron powder diffractometer) [pyrolitic graphite (002): λ = 2.458 Å, λ = 4.507 Å, and 2θstep = 0.1°] while ramping the temperature from 10 to 480 K. Longer acquisitions for magnetic structure refinements were made at 10 K. High-resolution patterns at both 10 and 300 K were also recorded at the powder diffractometer HRPT (high-resolution powder diffractometer for thermal neutrons) [Ge (822): 2θstep = 0.05° and λ = 1.154 Å] and D2B (high-resolution two-axis diffractometer) [Ge (335): 2θstep = 0.05° and λ = 1.594 Å]. The wavelengths and zero offsets were determined using a NAC (Na2Al12Ca3F14) reference powder sample. In the case of DyBaCuFeO5, the impact of the relatively large neutron absorption cross section of natural dysprosium [994(13) barn] in the data was corrected by including in the refinements the μR values determined experimentally for the different wavelengths. The background from the sample environment was minimized through 5′ collimators (D2B) and an oscillating radial collimator (HRPT). The values of Tcollinear and Tspiral derived from this technique correspond, respectively, to the setup and the maximum of the magnetic Bragg reflection (1/2, 1/2, 1/2) that roughly coincide with the values determined from χDC and DSC (see figs. S1 and S2 and tables S1).

Data analysis

All diffraction data were analyzed using the Rietveld package FullProf Suite (50). The structural refinements for the REBaCuFeO5 series were carried out by combining both HRPT and D2B datasets recorded at RT and 10 K. For YBa1−xSrxCuFeO5 samples, HRPT data recorded at RT and 10 K were used for the fits of the crystal structure (fig. S6). The magnetic refinements were performed on DMC data recorded at 10 K by fixing the structural parameters as determined from the refinements of the HRPT and D2B patterns (fig. S5). We used the noncentrosymmetric space group P4mm for the description of the crystal structure. The choice was motivated by the fact that, contrary to the centrosymmetric space group P4/mmm, P4mm enables the refinement of the occupation of the split Cu and Fe sites.

The Cu/Fe disorder was described by splitting the atomic position (1/2, 1/2, z) inside the two pyramidal sites of the unit cell, as shown in tables S2 and S3. In the fully disordered case, both positions are equally occupied in all pyramids (i.e., nFe = nCu = 50%), whereas full Cu/Fe order corresponds to nCu = 100% and nFe = 0 (or nCu = 0 and nFe = 100%). As shown in tables S2 and S3, the samples investigated in this work are very close to the first scenario, i.e., of |nCu – nFe| very close to zero. Note that Rietveld fits are not sensible to occupational correlations. The Cu/Fe disorder is thus assumed to be random, and the refined nCu and nFe values represent the average values over the full sample.

Anisotropic Debye-Waller factors were used for all atoms with the exception of Y/RE (nearly isotropic) [see (21)], Cu, and Fe. The z coordinates of the two basal oxygen sites O2 and O2′ were refined separately, but their mean-square displacements were restricted to have the same value (tables S2 and S3). No signature of interstitial oxygen at the (1/2, 1/2, z) atomic position could be observed, indicating that deviations from the sample’s formula stoichiometry, if any, were within the detection limit of PND in all the samples investigated. For the YBa1−xSrxCuFeO5 sample with x = 0.5, we could not find any evidence of alternating Ba/Sr layers, recently predicted for x ≥ 0.5 (26) and easy to identify because of the associated doubling of the c lattice parameter.

The collinear and spiral magnetic structures were described according to the models reported in (18). The best fits obtained at 10 K for all samples are shown in fig. S5. The ratio between the Fe3+(3d5 HS) and Cu2+(3d9) magnetic moments was restricted to be the same as their free-ion, spin-only values (5:1). In the temperature regions where the collinear and spiral phases coexist, the Fe and Cu magnetic moments were restricted to have the same value and the same inclination with respect to the ab plane in the two magnetic phases.

Table S2. Results of the Rietveld fits of the PND patterns for the REBaCuFeO5 (RE = Lu to Dy) family at RT and 10 K.

Table S3. Results of the Rietveld fits of the PND patterns for YBa1−xSrxCuFeO5 (x = 0 to 0.5) family at RT and 10 K.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

Acknowledgments: We thank A. Scaramucci, M. Müller, Ch. Mudry, N. Spaldin, M. Shi, Z. Wang, M. Radovic, J. Mesot, R. Sibille, and T. Mazet for fruitful discussions. We acknowledge the allocation of beam time at SINQ (HRPT and DMC diffractometers) and ILL (D2B diffractometer; https://search.datacite.org/data-centers/inist.ill?registered=2018&page=1). E.C. acknowledges support from the Danish Research Council for Science and Nature through DANSCATT. Funding: This work was supported by the Swiss National Science Foundation (grant nos. 200021_141334 and 206021_139082). Author contributions: T.S. and M.Me. conceived and led the project. T.S., M.Mo., and E.P. synthesized the samples. T.S., E.C., M.Me., D.S., and M.T.F.-D. performed the PND measurements. T.S. measured the magnetic susceptibility and DSC. T.S. and M.Me. analyzed all the experimental data. T.S. and M.Me. wrote the paper with input from all authors. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors. Raw powder diffraction data were generated at the SINQ (Paul Scherrer Institut, Switzerland) and ILL (Grenoble, France). Derived data supporting the results of this study are available from the corresponding authors. FullProf Suite is available free of charge at www.ill.eu/sites/fullprof.